Introduction

0Introduction01:51

Circular Trigonometry

1Lesson 1 - Angles Measured in Radians or Degrees07:00

Objectives: 1. Convert an angle between degrees and radians 2. Draw an angle in standard position

1Lesson 1 - Worksheet Review00:00

2Lesson 2 - Introducing Sine and Cosine23:00

Objectives:
1. Find the exact value of sine and cosine given an angle
2. Find the exact value of sine and cosine given an angle passing through a point

2Lesson 2 - Worksheet Review14:53

3Lesson 3 - Sine and Cosine using the Unit Circle07:34

Objectives:
1. Find the exact value of sine and cosine using a unit circle
2. Use the unit circle to find an angle that gives a specified trig ratio

3Lesson 3 - Worksheet Review03:20

4Lesson 4 - Inverse Sine and Cosine Functions09:17

Objectives:
1. Find the exact value of an inverse sine or cosine function.
2. Simplify an expression with inverse sine or cosine.
3. Use a calculator to find an approximate value of an inverse sine or cosine function.

21Lesson 21 - Worksheet Review06:55

22Lesson 22 - Vectors in Cartesian Coordinates I19:54

Objectives:
1. Define vector between two points
2. Find the magnitude of a vector
3. Find the direction of a vector
4. Find a unit vector that goes in the same direction as a given vector

22Lesson 22 - Worksheet Review15:13

23Lesson 23 - Vectors in Cartesian Coordinates II17:27

Objectives:
1. Apply addition, subtraction and scalar multiplication to vectors
2. Find the dot product between two vectors
3. Find the angle between two vectors

23Lesson 23 - Worksheet Review12:11

24Lesson 24 - Vectors in Polar Coordinates08:11

Objectives:
1. Find the components of a vector given its magnitude and angle
2. Add two vectors given their magnitudes and angles

24Lesson 24 - Worksheet Review06:50

25Lesson 25 - Complex Numbers I09:25

Ojectives:
1. Simplify the square root of negative numbers using the imaginary number i
2. Find the complex conjugate of a complex number
3. Graph a complex number in the complex plane
4. Find the magnitude of a complex number

25Lesson 25 - Worksheet Review05:50

26Lesson 26 - Complex Numbers II15:40

Ojectives:
1. Find the magnitude of a complex number
2. Find the angle of a complex number
3. Write a complex number in trigonometric form

Pre-calculus weaves together previous study of algebra, geometry, and functions into a preparatory course for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. Topics include trigonometric ratios and functions; inverse trigonometric functions; applications of trigonometry, including vectors and laws of cosine and sine; polar functions and notation; and arithmetic of complex numbers. Particular emphasis is placed on students' ability to reason critically on their own without the use of technology. The tests are broken into two parts: Part 1 covers problems that can be solved without technology and Part 2 covers problems that can be solved with technology.

Course Goals

Upon completion of this course, students will be prepared to move on to Calculus. Students will be able to apply trigonometry, vectors, polynomials and matrices to a variety of situations.

Course Requirements

Student taking this course are expected to have mastered the most important topics taught in an Algebra 2 course. Important topics to master are:

Factoring

Solving Linear/Quadratic Equations

Plotting points and graphs in the Cartesian Plane

Target Audience

This video course is primarily intended for students who have already mastered Algebra 2 concepts(typically 16+) and are planning on taking Calculus or for students in Precalculus or Calculus and need to review previously taught concepts (typically 17+).

Technology

The majority of the lessons are taught so that technology is not needed. However there are some where the use of a calculator or computer is required. Under the Additional Resources for Parents are tutorial videos that show how to use either online resources or a calculator to perform the work needed. The free online resources used are www.wolframalpha.com and www.desmos.com. The calculator used is the TI-83 which is the most commonly used graphing calcuculator in schools. If you use any TI calculator with the number 83 or 84, the instructions will be fine.

Course Includes

18 hours of video

41 video lessons

41 skill worksheets

41 worksheet review videos

41 online lesson quizzes

2 tests (Additional Resources for Parents)

Answer keys to all tests (Additional Resources for Parents)

Blank Lesson Notes Sheets for all lessons

Completed Lesson Notes (Additional Resources for Parents)

Completed Worksheet Problems (Additional Resources for Parents)

Course Topics

Angles Measured in Radians or Degrees

Introducing Sine and Cosine

Sine and Cosine using the Unit Circle

Inverse Sine and Cosine Functions

Graphing Trigonometric Functions I

Graphing Trigonometric Functions II

Modeling Trigonometric Functions

Tangent and Cotangent Functions

Tangent and Slope

Secant and Cosecant Functions

Pythagorean Identity

Addition Formulas for Sines and Cosines

Half Angle and Double Angle Formulas

Proving other Trigonometric Identities

Right Triangle Trigonometry

Law of Sines and Law of Cosines

Ambiguous Case for Law of Sines

Determining the Area of a Triangle

Applying Trigonometry

Polar Coordinates

Converting Points

Vectors in Cartesian Coordinates I

Vectors in Cartesian Coordinates II

Vectors in Polar Coordinates

Complex Numbers I

Complex Numbers II

Arithmetic of Complex Numbers

DeMoivre's Theorem

Introduction to Linear Algebra and Matrices

Row Operations of a Matrix

Row Echelon and Reduced Row Echelon Form

Coefficient Matrices

Gaussian and GaussJordan Elimination

Addition on Matrices and Vectors

Matrix Multiplication

Proofs by Mathematical Induction

Zeros and Factors of Polynomials

Rational Root Theorem

Synthetic Division

Repeated Zeros of a Polynomial

Fundamental Theorem of Algebra

Teacher: Jim

Areas of expertise: Mathematics, Spanish, Technology

Education: Augustana College
St. Ambrose University

Interests: Board Gaming

Skills: Singing

Associations: National Council of Teachers of Mathematics, Illinois Council of Teachers of Mathematics

Issues I care about:

I want to make the world a better place by helping those around me reach their full potential. If we all do our best to help everyone do their best, the world would be a much better place.

Lesson 1 - Angles Measured in Radians or Degrees

This contains:
1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 2 - Introducing Sine and Cosine

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 2 - Introducing Sine and Cosine - Calculator Supplement

This video shows how to use the calculator for Introducing Sine and Cosine

Lesson 2 - Introducing Sine and Cosine - Computer Supplement

This video shows how to use the computer for Introducing Sine and Cosine

Lesson 3 - Sine and Cosine using the Unit Circle

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 4 - Inverse Sine and Cosine Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 4 - Inverse Sine and Cosine Function - Calculator

This video shows how to use the calculator for Inverse Sine and Cosine Functions

Lesson 4 - Inverse Sine and Cosine Function - Computer

This video shows how to use the computer for Inverse Sine and Cosine Functions

Lesson 5 - Graphing Trigonometric Functions I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 5 - Graphing Trigonometric Functions I - Calculator

This video shows how to use the calculator for Graphing Trigonometric Functions I

Lesson 5 - Graphing Trigonometric Functions I - Computer

This video shows how to use the computer for Graphing Trigonometric Functions I

Lesson 6 - Graphing Trigonometric Functions II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 6 - Graphing Trigonometric Functions II - Calculator

This video shows how to use the calculator for Graphing Trigonometric Functions II

Lesson 6 - Graphing Trigonometric Functions II - Computer

This video shows how to use the computer for Graphing Trigonometric Functions II

Lesson 7 - Modeling Trigonometric Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 8 - Tangent and Cotangent Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 9 - Tangent and Slope

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 10 - Secant and Cosecant Functions

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 11 - Pythagorean Identity

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 12 - Addition Formulas for Sines and Cosines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 13 - Half-Angle and Double-Angle Formulas

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 14 - Proving other Trigonometric Identities

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 15 - Right Triangle Trigonometry

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 16 - Law of Sines and Law of Cosines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 17 - Ambiguous Case for Law of Sines

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 18 - Determining the Area of a Triangle

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 19 - Applying Trigonometry

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Midterm Exam

This exam covers the first 19 lessons of the course. It is administered in two parts:

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed.This section should take no more than 60 minuts to complete.

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete.

Topics to focus on:

Angles in Radians and Degrees

Sine and Cosine using the Unit Circle

Graphing Trigonometric Functions

Tangent, Cotangent, Secant and Cosecant Functions

Half-Angle Identities of Sine and Cosine

Addition Formulas for Sine and Cosine

Proving Trigonometric Identities

Tangent and Slope

Right Triangle Trigonometry

Law of Sines and Law of Cosines

Determining the Area of a Triangle

Lesson 20 - Polar Coordinates

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 21 - Converting Points

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 22 - Vectors in Cartesian Coordinates I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 23 - Vectors in Cartesian Coordinates II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 24 - Vectors in Polar Coordinates

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 25 - Complex Numbers I

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 26 - Complex Numbers II

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 27 - Arithmetic of Complex Numbers

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 28 - DeMoivre's Theorem

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 29 - Introduction to Linear Algebra and Matrices

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 30 - Row Operations of a Matrix

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 31 - Row Echelon and Reduced Row Echelon Form

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Lesson 31 - Row Echelon and Reduced Row Echelon Form - Calculator

This video shows how to use the calculator for Row Echelon and Reduced Row Echelon Form

Lesson 31 - Row Echelon and Reduced Row Echelon Form - Computer

This video shows how to use the computer for Row Echelon and Row Echelon Form

Lesson 32 - Coefficient Matrices

This contains: 1) The completed lesson notes 2) The worked out solutions to the worksheet problems

Final Exam

This exam covers the entire 41 lessons of the course, focusing on the lessons 20-41.

Part 1 is intended to be done without the assistance of a calculator or computer. The use of the unit circle is allowed. This section should take no more than 75 minuts to complete.

Part 2 is intended to be done with the aid of a calculator or computer. This section should take no more than 45 minuts to complete.